Point and Interval Estimate by regi.pptx

A ppt lesson about estimation

1. Point Estimate And Interval Estimate

2. 1. Define what is: a. Parameter b. Estimate 2. Differentiate the point estimate and Interval Estimate Objective:

3. - a numerical characteristic of a population , as distinct from a  statistic  of a sample. ? Parameter

4. Ex. A number of students in CKC A number of population in Brgy . Matobato Parameter

5. A value, or range of values, that approximates the population ? Estimate

6. 2 Types Point Estimate It is a specific numerical value of a population parameter The sample mean is the best point estimate of a population mean.   Interval Estimate Also called as confidence interval , a range values used to estimate a parameter. This estimate may or may not contain the true parameter value .

7. Point Estimate Ex. Jacky wanted to know the average students in statistics. She interviewed 40 students and the results are shown on the right.

8. Interval Estimate When σ is known The confidence level of an interval estimate is the probability that the interval estimate will contain the true population parameter. - How sure are we that the population parameter is really within that we came up with.

9. Interval Estimate – 2 ways 1.) When σ is known The confidence level of an interval estimate is the probability that the interval estimate will contain the true population parameter. - How sure are we that the population parameter is really within that we came up with.

10. Interval Estimate – 2 ways 2.) When σ is unknown When σ is unknown, the interval estimate can be determined using the student’s t-distribution .

11. Interval Estimate : σ is known

12. Interval Estimate E – Margin of Error Z - critical value/z- value σ – population standard deviation or sigma N – sample size

13. Interval Estimate Lower limit Upper Limit

14. Solve for Interval Estimate Example: Step 1: Determine the given values Step 2: Determine the critical value Step 3: Solve for the margin of error using the formula Step 4: Solve for the Interval estimate Procedure:

15. Solve for Interval Estimate Example: Given: Sample size ( n ) = 100 Sample mean = 150 Population SD σ = 40 Confidence level = 95% = critical value: Z =1.96  

16. Solve for Interval Estimate Example: Given: Sample size ( n ) = 50 Sample mean = 20.5 Population SD σ = 3.7 Confidence level = 99% = critical value: Z = 2.58  

17. Interval Estimate – #2 way/ method 2.) When σ is unknown When σ is unknown, the interval estimate can be determined using the student’s t-distribution .

18. Interval Estimate – σ is unknown Where; n – is the sample size

19. Interval Estimate – σ is unknown

20. Interval Estimate – σ is unknown (Example) Step 1: Determine the given values Step 2: Determine the degrees of freedom using the formula and the t (using the table) Step 3: Solve for the margin of error using the formula Step 4: Solve for the Interval estimate Procedure:

21. Interval Estimate – σ is unknown (Example) Given: Sample size ( n ) = 30 Sample mean = 5.3 Sample S = 1.1 Confidence level = 95% Degrees of freedom = n – 1 = 30 – 1 = 29  

22. Interval Estimate – σ is unknown (Example)

23. ESTIMATING SAMPLE SIZE In order to determine the sample size we follow the formula: n =   Where; n = sample size = Z values E = margin error  

24. ESTIMATING SAMPLE SIZE In order to determine the sample size we follow the formula: n =   Where; n = sample size = Z values E = margin error  

25. QUIZ !!! 1 whole sheet of paper -YES, 1 whole

26. Direction: Solve for the Point Estimate 95 85 85 90 88 80 88 87 82 92 90 91 88 94 90 92 89 90 96 89 84 90 85 87 95 96 94 93 94 90 89 88 89 85 86 92 Mr. Gonzales wanted to know the average students in statistics. He interviewed 36 students and the results are shown below.

27. Direction: Solve for the Interval Estimate. In a study of 80 junior high school students, the mean number of hours per week that they used internet was 40 hours. It was estimated that the population standard deviation was 2.5. What is the 95% confidence interval for the mean time for using internet?

28. THANK YOU !!!